Blender 2.8 edit mode. I can see through parts of my model
A little more information and visual examples would be helpful to verify exactly what is going on. It could be a couple things. Could be a feature or a bug(given the fact that 2.8 is still in beta). I want to lean more towards a possible bug.

There is a feature that can do what it sounds like you might be describing, in terms of "seeing through the mesh". However it appears disabled in your Header at the bottom of the viewport.

The button in the Header  allows you to make the whole scene transparent when enabled. Therefore see through the mesh. But only seeing the face dots and not the wireframe is why I think its a bug.

Image 1 transparency of the scene is disabled.


Image 2 transparency is enabled.


According to your image you are using v2.80.39. I am using v2.80.45 and cannot recreate your issue exactly.

I would recommend updating to a newer version of the beta(nightly builds), and see if the issue remains.

I could be wrong, but unless someone else can state otherwise and educate us both, I'm guessing its a bug.